A certain truck can tow a trailer if the combined weight of the trailer and the packages it contains is no more than 5,600 pounds. What is the maximum number of packages this truck can tow in a trailer with a weight of 600 pounds if each package weighs 130 pounds?

To solve this problem, we need to determine the maximum number of packages the truck can tow without exceeding the combined weight limit of 5,600 pounds.

### Step-by-Step Solution:

1. **Understand the total weight constraint**:  
   The truck can tow a maximum combined weight (trailer + packages) of **5,600 pounds**.

2. **Weight of the trailer**:  
   The trailer alone weighs **600 pounds**.

3. **Weight available for the packages**:  
   Subtract the weight of the trailer from the total weight limit to find out how much weight is available for the packages:
   \[
   5,600 - 600 = 5,000 \text{ pounds}
   \]

4. **Weight of each package**:  
   Each package weighs **130 pounds**.

5. **Calculate the maximum number of packages**:  
   To find out how many packages can be accommodated without exceeding the 5,000 pounds limit, divide the available weight by the weight of each package:
   \[
   \text{Maximum number of packages} = \left\lfloor \frac{5,000}{130} \right\rfloor
   \]

   Perform the division:
   \[
   \frac{5,000}{130} \approx 38.46
   \]

   Since we can only carry whole packages, we take the **floor** value of 38.46, which is **38**.

### Conclusion:

The **maximum number of packages** the truck can tow in the trailer without exceeding the weight limit is **38**.

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Would you like more details or have any questions about this solution?

### Additional Related Questions:

1. What would be the maximum number of packages if each package weighed 150 pounds instead?
2. How would the answer change if the trailer weight increased to 800 pounds?
3. What is the total weight of the trailer and packages when the truck carries the maximum number of packages?
4. If the weight limit was increased to 6,000 pounds, what would be the new maximum number of packages?
5. What is the weight per package required if the truck has to carry 40 packages within the 5,600 pounds limit?

### Tip:

Always check the maximum allowable weight constraints in problems involving carrying or towing to ensure you're within safe or permissible limits.

Discover how to calculate the maximum number of packages a truck can tow in a trailer without exceeding weight limits. This math problem involves arithmetic and division, with a step-by-step solution provided. Suitable for students in Grades 4-6.

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